Additionally, as the communal number pair \((N_\uparrow ,N_\downarrow )\)  is a function of the spin imbalance, multiple phase transitions through several superconducting phases should be observed as the imbalance is increased. Each transition is expected to be second order, and so the communal superconducting phase would be characterized by a series of singularities in the heat capacity and the compressibility, which should be directly observable in ultracold atomic gases [1]} as the spin-imbalance is changed. No such phase transitions are expected for the FFLO phase at fixed temperature.
